Okay, so let's talk strategies
I've only been playing as the TEC against the AI, but I found the following things useful:
* Build the cap-ship as soon as possible (ie. first structure after the refinaries). The first cap ship is free, and is enough for you to start expanding into lightly defended unclaimed colonies. You can add a few frigates to the group afterwards, to take on the more heavily defended ones.
* Expand the fleet capacity very cautiously: Early on what you really want is to build up your economy, expanding quickly until you reach other players. Having too large a support will eat into your resources, so only upgrade if you're currently at capacity and your fleet is not sufficient.
* Get the heavy cruiser quickly: One of the first things I do, after I have 2 or 3 colonies, is place down 5 military research structures and research the kodiak heavy cruiser. By using high-end units quickly I can keep my support cap lower, and so keep more of my resources.
* Look for 'choke points', capture them and defend them heavily. Identify the systems which are entrances into your empire, and attempt to minimise the number of these systems you own. Once you have a good choke point, place a lot of point defenses around.
* Point defenses are very good in border systems. They are pretty cheap (2 gauss turrets is a similar cost to a single heavy cruiser), and they don't add to the support cap. Having plenty of point defenses in a system will bog down even a large fleet for long enough for your re-enforcements to arrive from neighbouring sectors.
* Fleets don't need to be in every border sector, just within one or two jumps. With sufficient point defenses one fleet can often service several entrance points, allowing you to use less ships total and attack with greater force every time. Again, the point defenses aren't there to kill the enemy fleet, just to keep them occupied long enough for your forces to jump in and clear up.
* Decide early on which lines you are going to defend, and from which you will attack. A war on two fronts is not desirable. Send pirates to the enemy you are going to attack, and if possible make friends with the other(s) which border you. You can still make hit-and-run attacks into a (non-allied) enemy territory that you are defending against, but focus your colonisation and advancement efforts in one place.
* Don't be afraid of losing fleets. With the support cap resource cost, maintaining a smaller fleet means you can replenish quickly. Often you can send in your fleet against a slightly superior force, and replenish your forces into a neighbouring system (from two or three surrounding systems with frigate facilities). By the time the first fleet becomes heavily out-numbered, you have a new fleet of similar size ready to jump in and finish off the weakened enemy. Although you both lose ships heavily, your smaller fleet allows you to recover more quickly, so in the long-term it is a win.
* Watch enemy fleet movements. The AI likes to keep a single main fleet (at least early on anyway), so if you see that preoccupied with one of your fleets, or an AI fleet, try to send in a few frigates to systems far from it, for hit-and-run attacks. No need to take the planet (or even wipe it out unless you have a shedload of seige frigates handy), just interfere with the enemy economy.
Okay, that's a few things I found useful. I imagine against a human opponent you would want to be a bit more aggressive, or pay the penalty. But still. Anyone else care to share their strategies?